Chapter 8

Exercise 8.1

  1. AK-8.1-1
  1. AK-8.1-3

    1. Quadrant II


    2. Quadrant IV


    3. Quadrant I


    1. X-axis (left)


    2. Quadrant III


    3. Y-axis (up)


    1. 2 units

      AK-8.1-9a

    2. 9 units

      AK-8.1-9b

    1. 5 units

      AK-8.1-11a

    2. 8 units

      AK-8.1-11b

    1. 5 units

      AK-8.1-13a

    2. 7 units

      AK-8.1-13b

    1. 4 units

      AK-8.1-15a

    2. 6 units

      AK-8.1-15b

  1. D (–3, –1)


  1. S(–3, –1)


  1. (1, 12) and (1, –2)


  1. (–7, 3) and (5, 3)


Exercise 8.2

    1. 4


    2. 10


    3. 6


    4. 9


    5. 15


    6. 6


    1. –3


    2. 3


    3. 1


    4. [latex] \displaystyle{\frac{3}{2}} [/latex]


    5. 6


    6. –6


  1. [latex] 5x - 2y = -2 [/latex]


  1. [latex] 3x + 4y = -12 [/latex]


  1. [latex] x - 2y = -3 [/latex]


  1. [latex] \displaystyle{y = -\frac{3}{2}x - \frac{3}{4}} [/latex]


  1. [latex] \displaystyle{y = \frac{3}{2}x + 5} [/latex]


  1. [latex] \displaystyle{y = -\frac{3}{2}x + 3} [/latex]


  1. [latex] y = x + 3 [/latex]
    [latex] x [/latex] [latex] y [/latex] [latex] (x, y) [/latex]
    [latex] 0 [/latex] [latex] 3 [/latex] [latex] (0, 3) [/latex]
    [latex] 1 [/latex] [latex] 4 [/latex] [latex] (1, 4) [/latex]
    [latex] 2 [/latex] [latex] 5 [/latex] [latex] (2, 5) [/latex]
    [latex] 3 [/latex] [latex] 6 [/latex] [latex] (3, 6) [/latex]

    AK-8.2-17
  1. [latex] y = -5x + 1 [/latex]
    [latex] x [/latex] [latex] y [/latex] [latex] (x, y) [/latex]
    [latex] 0 [/latex] [latex] 1 [/latex] [latex] (0, 1) [/latex]
    [latex] 1 [/latex] [latex] -4 [/latex] [latex] (1, -4) [/latex]
    [latex] 2 [/latex] [latex] -9 [/latex] [latex] (2, -9) [/latex]
    [latex] 3 [/latex] [latex] -14 [/latex] [latex] (3, -14) [/latex]

    AK-8.2-19
  1. [latex] 2x + y + 1 = 0 [/latex]
    [latex] x [/latex] [latex] y [/latex] [latex] (x, y) [/latex]
    [latex] 0 [/latex] [latex] -1 [/latex] [latex] (0, -1) [/latex]
    [latex] 1 [/latex] [latex] -3 [/latex] [latex] (1, -3) [/latex]
    [latex] 2 [/latex] [latex] -5 [/latex] [latex] (2, -5) [/latex]
    [latex] 3 [/latex] [latex] -7 [/latex] [latex] (3, -7) [/latex]

    AK-8.2-21
  1. [latex] 2x - y - 3 = 0 [/latex]
    [latex] x [/latex] [latex] y [/latex] [latex] (x, y) [/latex]
    [latex] 0 [/latex] [latex] -3 [/latex] [latex] (0, -3) [/latex]
    [latex] 1 [/latex] [latex] -1 [/latex] [latex] (1, -1) [/latex]
    [latex] 2 [/latex] [latex] 1 [/latex] [latex] (2, 1) [/latex]
    [latex] 3 [/latex] [latex] 3 [/latex] [latex] (3, 3) [/latex]

    AK-8.2-23

  1. x-intercept: [latex] \displaystyle{(-\frac{2}{3}, 0)} [/latex]; y-intercept: [latex] \displaystyle{(0, -2)} [/latex]


    AK-8.2-25

  1. x-intercept: [latex] 7, 0 [/latex]; y-intercept: [latex] 0, 7 [/latex]


    AK-8.2-27

  1. x-intercept: [latex] -2, 0 [/latex]; y-intercept: [latex] 0, 4 [/latex]


    AK-8.2-29

  1. [latex] \displaystyle{m = \frac{2}{3}; b = -6} [/latex]


    AK-8.2-31

  1. [latex] \displaystyle{m = \frac{4}{7}; b = 3} [/latex]


    AK-8.2-3

  1. Positive slope



  1. 0


  1. [latex] \displaystyle{-\frac{5}{8}} [/latex]


  1. [latex] y = 2 [/latex]


  1. [latex] y = x - 2 [/latex]


  1. [latex] y = -2x + 10 [/latex]


  1. [latex] \displaystyle{y = \frac{2}{3}x} [/latex]


  1. [latex] \displaystyle{y = -\frac{3}{2}x + 6} [/latex]


  1. 2


  1. 7


  1. [latex] 5x + 3y = 15 [/latex]


  1. [latex] 2x + y = 1 [/latex]


  1. Perpendicular


  1. Parallel


  1. Perpendicular


  1. Neither


  1. [latex] \displaystyle{y = \frac{2}{3}x - \frac{13}{3}} [/latex]


  1. [latex] \displaystyle{y = \frac{1}{3}x - 20} [/latex]


  1. [latex] y = x + 7 [/latex]


  1. [latex] \displaystyle{y = -\frac{1}{2}x + 1} [/latex]


Review Exercises 8

    1. Quadrant IV


    2. Quadrant II


    3. X-axis (right)


    4. Quadrant IV


    5. X-axis (right)


    6. Y-axis (up)


  1. Rectangle

    Perimeter = 22 units; Area=24 square units


    AK-RE-3
  1. [latex] 4x - y = 2 [/latex]
    [latex] x [/latex] [latex] y [/latex] [latex] (x, y) [/latex]
    [latex] 0 [/latex] [latex] -2 [/latex] [latex] (0, -2) [/latex]
    [latex] 1 [/latex] [latex] 2 [/latex] [latex] (1, 2) [/latex]
    [latex] 2 [/latex] [latex] 6 [/latex] [latex] (2, 6) [/latex]
    [latex] 3 [/latex] [latex] 10 [/latex] [latex] (3, 10) [/latex]

    AK-RE-5
  1. [latex] x + y - 4 = 0 [/latex]
    [latex] x [/latex] [latex] y [/latex] [latex] (x, y) [/latex]
    [latex] 0 [/latex] [latex] 4 [/latex] [latex] (0, 4) [/latex]
    [latex] 1 [/latex] [latex] 3 [/latex] [latex] (1, 3) [/latex]
    [latex] 2 [/latex] [latex] 2 [/latex] [latex] (2, 2) [/latex]
    [latex] 3 [/latex] [latex] 1 [/latex] [latex] (3, 1) [/latex]

    AK-RE-7
  1. [latex] \displaystyle{y = \frac{1}{2}x + 2} [/latex]
    [latex] x [/latex] [latex] y [/latex] [latex] (x, y) [/latex]
    [latex] 0 [/latex] [latex] 2 [/latex] [latex] (0, 2) [/latex]
    [latex] 2 [/latex] [latex] 3 [/latex] [latex] (2, 3) [/latex]
    [latex] 4 [/latex] [latex] 4 [/latex] [latex] (4, 4) [/latex]
    [latex] 6 [/latex] [latex] 5 [/latex] [latex] (6, 5) [/latex]

    AK-RE-9
  1. [latex] 3x - 4y = 12 [/latex]
    [latex] x [/latex] [latex] y [/latex] [latex] (x, y) [/latex]
    [latex] 0 [/latex] [latex] -3 [/latex] [latex] (0, -3) [/latex]
    [latex] 4 [/latex] [latex] 0 [/latex] [latex] (4, 0) [/latex]
    [latex] 8 [/latex] [latex] 3 [/latex] [latex] (8, 3) [/latex]

    AK-RE-11
  1. [latex] x - 2y - 6 = 0 [/latex]
    [latex] x [/latex] [latex] y [/latex] [latex] (x, y) [/latex]
    [latex] 0 [/latex] [latex] -3 [/latex] [latex] (0, -3) [/latex]
    [latex] 6 [/latex] [latex] 0 [/latex] [latex] (6, 0) [/latex]
    [latex] 2 [/latex] [latex] -2 [/latex] [latex] (2, -2) [/latex]

    AK-RE-13
  1. [latex] x - 2y - 6 = 0 [/latex]
    [latex] x [/latex] [latex] y [/latex] [latex] (x, y) [/latex]
    [latex] 0 [/latex] [latex] -3 [/latex] [latex] (0, -3) [/latex]
    [latex] 6 [/latex] [latex] 0 [/latex] [latex] (6, 0) [/latex]
    [latex] 2 [/latex] [latex] -2 [/latex] [latex] (2, -2) [/latex]

    AK-RE-13
  1. [latex] y = 4x [/latex]
    [latex] x [/latex] [latex] y [/latex] [latex] (x, y) [/latex]
    [latex] 0 [/latex] [latex] 0 [/latex] [latex] (0, 0) [/latex]
    [latex] 1 [/latex] [latex] 4 [/latex] [latex] (1, 4) [/latex]

    AK-RE-15

  1. [latex] m = 4; b = 6 [/latex]


    AK-RE-17

  1. [latex] \displaystyle{m = -\frac{3}{2}; b = 6} [/latex]


    AK-RE-19

  1. [latex] \displaystyle{m = -\frac{3}{4}; b = -1} [/latex]


    AK-RE-21

  1. [latex] \displaystyle{y = \frac{3}{4}x - \frac{1}{4}} [/latex]


  1. [latex] \displaystyle{y = -\frac{4}{3}x + \frac{8}{3}} [/latex]


  1. [latex] y = 3x - 5 [/latex]


  1. [latex] \displaystyle{y = \frac{3}{4}x + \frac{9}{2}} [/latex]


  1. [latex] y = -2x + 1 [/latex]


  1. [latex] (2, -5) [/latex]


    AK-RE-33

  1. [latex] (6, 2) [/latex]


    AK-RE-35

  1. [latex] (2, 1) [/latex]


    AK-RE-37

    1. Company A: [latex] y = 40x + 250 [/latex];

      Company B: [latex] y = 50x + 200 [/latex]


    2. AK-RE-39b

    3. [latex] (5, 450) [/latex]; both companies charge a total fee of $450 for 5 hours of labour


    4. Paul should hire Company A if the labour will take more than 5 hours


  1. One solution


  1. No solution


  1. Infinitely many solutions


  1. [latex] (4, 1) [/latex]


  1. [latex] \displaystyle{(\frac{52}{19}, -\frac{70}{19})} [/latex]


  1. [latex] (1, 1) [/latex]


  1. [latex] (2, 1) [/latex]


  1. [latex] (-4, -2) [/latex]


  1. [latex] (3, 0) [/latex]


  1. [latex] (3, 4) [/latex]


  1. [latex] (15, 20) [/latex]


  1. [latex] \displaystyle{(\frac{29}{7}, -\frac{13}{7})} [/latex]


  1. 65 and 30


  1. 210 adults, 90 kids


  1. 24 L; 36 L


  1. 2.29 km/h


  1. 2.5 hours


Self-Test Exercises 8

  1. [latex] (-3, -1) [/latex]; Area = 40 square units


    1. [latex] 2x - 3y = 6 [/latex]


    2. [latex] \displaystyle{x = \frac{25}{8}} [/latex]


    1. [latex] \displaystyle{y = \frac{2}{3}x = 2} [/latex]


    2. [latex] \displaystyle{y = -\frac{3}{4}x + \frac{5}{4}} [/latex]


  4. [latex] 2x - 3y = 9 [/latex]
    [latex] x [/latex] [latex] y [/latex] [latex] (x, y) [/latex]
    [latex] 0 [/latex] [latex] -3 [/latex] [latex] (0, -3) [/latex]
    [latex] 3 [/latex] [latex] -1 [/latex] [latex] (3, -1) [/latex]
    [latex] 6 [/latex] [latex] 1 [/latex] [latex] (6, 1) [/latex]
    [latex] 9 [/latex] [latex] 3 [/latex] [latex] (9, 3) [/latex]

    AK-STE-4
  5. [latex] 3y + 4x = 0 [/latex]
    [latex] x [/latex] [latex] y [/latex] [latex] (x, y) [/latex]
    [latex] 0 [/latex] [latex] 0 [/latex] [latex] (0, 0) [/latex]
    [latex] 3 [/latex] [latex] -4 [/latex] [latex] (3, -4) [/latex]
    [latex] 6 [/latex] [latex] 1 [/latex] [latex] (6, 1) [/latex]

    AK-STE-5
    1. AK-STE-6a
    2. AK-STE-6b

  7. [latex] 4x + 5y = 9 [/latex]


  8. [latex] 3x - 5y = 15 [/latex]


  9. [latex] 3x - 2y = -12 [/latex]


  10. [latex] \displaystyle{\frac{4}{3}x - y = 0} [/latex]


    1. Infinitely many solutions


    2. AK-STE-11

    1. Club A: [latex] y = 20x + 180 [/latex];

      Club B: [latex] y = 30x [/latex]


    2. AK-STE-12b

    3. [latex] (18, 540) [/latex]; both clubs charge a fee of $540 for 18 hours of court time


    4. Sandra should join club A if she is planning to play more than 18 hours


    1. One solution


    2. No solution


    3. No solution


  14. [latex] \displaystyle{(\frac{15}{7}, -\frac{18}{7})} [/latex]


  15. [latex] \displaystyle{(-\frac{3}{2}, -\frac{3}{2})} [/latex]


  16. 35 and 30


  17. 75 quarters


  18. 325 adult tickets


  19. 5 lb; 10 lb


  20. 4.5 km/h; 1.5 km/h